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ABC is a triangle inscribed in a circle, AC being the diameter of the circle. The length of AC is as much more than the length of BC as the length of BC is more than the length of AB. Find AC:AB.

7 years ago

Answers : (2)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points

Dear Vipul,

Solution:- Given, AC = a BC and BC = a AB. We want to find AC: AB  = a2

Since, AC is the diameter of the circle, it subtends 900 angle at B. Let, AC = 'd' and angle C be 'x'. Then,

AB = d sinx , and BC = d cosx

So, AC = a BC will give 1 = a cosx     or    cosx = 1/a

And, BC = a AB will give cos x = a sinx

Since, cos x = 1/a, sin x = √(a2 -1) / a

So, 1 = a √(a2 -1)          or         a4 - a2 -1 = 0

On solving quad. eq., we'll get - a2 = (√5 +1) / 2  [ANS]

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Priyansh Bajaj

7 years ago
vipul agrawal
19 Points

Dear Priyansh,

I would like to correct your solution as follows:-

As per question we have to assume that if AB = X and BC = X+k then AC = BC+ k or AC = X+2k. Then we have to find AC:BC which is equal to 5:3. I would request you to find it out for my son Vipul.

Thanking you.


F/o Master Vipul Agrawal.

7 years ago
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